In known high speed reciprocating or orbiting power sanders the sandpaper is backed up by a layer of felt or rubber-like sponge material cemented to the reciprocating or orbiting back-up plate of the sander. It is also known, as in Hutchins U.S. Pat. Nos. 3,510,992 and 3,892,091 to provide a sanding pad of closed pore sponge material having an irregularized surface to which the uncoated side of the sandpaper is cemented. Although such known sanding pads provide a resilient back-up for the sandpaper for uniform distribution of pressure of the sandpaper against the work, the sandpaper rather quickly becomes clogged with build-up of sanded material thereon. Furthermore, sanders equipped with such known sanding pads do not effectively sand away high spots in the work and it is difficult and time consuming to achieve glass-smooth finishes on the work.